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In response to a community prediction challenge, we simulate the nonadiabatic dynamics of cyclobutanone using the mapping approach to surface hopping (MASH). We consider the first 500 fs of relaxation following photoexcitation to the S2 state and predict the corresponding time-resolved electron-diffraction signal that will be measured by the planned experiment. 397 ab initio trajectories were obtained on the fly with state-averaged complete active space self-consistent field using a (12,11) active space. To obtain an estimate of the potential systematic error, 198 of the trajectories were calculated using an aug-cc-pVDZ basis set and 199 with a 6-31+G* basis set. MASH is a recently proposed independent trajectory method for simulating nonadiabatic dynamics, originally derived for two-state problems. As there are three relevant electronic states in this system, we used a newly developed multi-state generalization of MASH for the simulation: the uncoupled spheres multi-state MASH method (unSMASH). This study, therefore, serves both as an investigation of the photodissociation dynamics of cyclobutanone, and also as a demonstration of the applicability of unSMASH to ab initio simulations. In line with previous experimental studies, we observe that the simulated dynamics is dominated by three sets of dissociation products, C3H6 + CO, C2H4 + C2H2O, and C2H4 + CH2 + CO, and we interpret our predicted electron-diffraction signal in terms of the key features of the associated dissociation pathways. [ABSTRACT FROM AUTHOR]

This paper introduces a spin-free formulation of the supporting subspace factorization [C. Song and T. J. Martínez, J. Chem. Phys. 149, 044108 (2018)], enabling a reduction in the computational scaling of the extended multi-state complete active space second-order perturbation (XMS-CASPT2) method for arbitrary spins. Compared to the original formulation that is defined in the spin orbitals and is limited to singlet states, the spin-free formulation in this work treats different spin states equivalently, thus naturally generalizing the idea beyond singlet states. In addition, we will present a new way of deriving the supporting subspace factorization with the purpose of understanding its physical interpretation. In this new derivation, we separate the sources that make CASPT2 difficult into the "same-site interactions" and "inter-site interactions." We will first show how the Kronecker sum can be used to remove the same-site interactions in the absence of inter-site interactions, leading to MP2 energy in dressed orbitals. We will then show how the inter-site interactions can be exactly recovered using Löwdin partition, where the supporting subspace concept will naturally arise. The new spin-free formulation maintains the main advantage of the supporting subspace factorization, i.e., allowing XMS-CASPT2 energies to be computed using highly optimized MP2 energy codes and Fock build codes, thus reducing the scaling of XMS-CASPT2 to the same scaling as MP2. We will present and discuss results that benchmark the accuracy and performance of the new method. To demonstrate how the new method can be useful in studying real photochemical systems, the supporting subspace XMS-CASPT2 is applied to a photoreaction sensitive to magnetic field effects. The new spin-free formulation makes it possible to calculate the doublet and quartet states required in this particular photoreaction mechanism. [ABSTRACT FROM AUTHOR]

The study and modeling of water exchange in complex media using different applications of diffusion and relaxation magnetic resonance (MR) have been of interest in recent years. Most models attempt to describe this process using a first order kinetics expression, which is appropriate to describe chemical exchange; however, it may not be suitable to describe diffusion-driven exchange since it has no direct relationship to diffusion dynamics of water molecules. In this paper, these limitations are addressed through a more general exchange expression that does consider such important properties. This exchange fraction expression features a multi-exponential recovery at short times and a mono-exponential decay at long times, both of which are not captured by the first order kinetics expression. Furthermore, simplified exchange expressions containing partial information of the analyzed system's diffusion and relaxation processes and geometry are proposed, which can potentially be employed in already established estimation protocols. Finally, exchange fractions estimated from simulated MR data and derived here were compared, showing qualitative similarities but quantitative differences, suggesting that the features of the derived exchange fraction in this paper can be partially recovered by employing an existing estimation framework. [ABSTRACT FROM AUTHOR]

Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586–599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head–tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes. [ABSTRACT FROM AUTHOR]

The current study examined the acquisition, retention, and transfer effects of a motor program. Children with autism spectrum disorder participated in a 9-week program that targeted 13 fundamental motor skills based upon the Test of Gross Motor Development-3. Assessments were conducted before and after the program, as well as at 2-month follow-up. Significant improvements were found on not only the trained fundamental motor skills (acquisition) but also the untrained tasks on balance (transfer). The follow-up tests revealed continuous improvement on the trained locomotor skills (retention), as well as the untrained skills on balance (retention + transfer). These findings highlight the importance of continuous support and long-term participation on motor practices. [ABSTRACT FROM AUTHOR]

The adiabatic connection formalism, usually based on the first-order perturbation theory, has been generalized to an arbitrary order. The generalization stems from the observation that the formalism can be derived from a properly arranged Taylor expansion. The second-order theory is developed in detail and applied to the description of two electrons in a parabolic confinement (harmonium). A significant improvement relative to the first-order theory has been obtained. [ABSTRACT FROM AUTHOR]

We consider a voting scenario in which the resource to be voted upon may consist of both indivisible and divisible goods. This setting generalizes both the well-studied model of multiwinner voting and the recently introduced model of cake sharing. Under approval votes, we propose two variants of the extended justified representation (EJR) notion from multiwinner voting, a stronger one called EJR for mixed goods (EJR-M) and a weaker one called EJR up to 1 (EJR-1). We extend three multiwinner voting rules to our setting—GreedyEJR, the method of equal shares (MES), and proportional approval voting (PAV)—and show that while all three generalizations satisfy EJR-1, only the first one provides EJR-M. In addition, we derive tight bounds on the proportionality degree implied by EJR-M and EJR-1, and investigate the proportionality degree of our proposed rules. [ABSTRACT FROM AUTHOR]

Trust is one of the highly important concepts of consumer research; yet it is characterized by a striking lack of generalizations and consensus regarding the relative strength of its antecedents, consequences, and moderators. To close this important gap, the current research reports a comprehensive large-scale meta-analysis shedding light on a wide variety of the antecedents, consequences, and moderators of the individual consumer's trust and their relative importance. Empirical generalizations are based on 2,147 effect sizes from 549 studies across 469 manuscripts in numerous disciplines, representing a total of 324,834 respondents in 71 countries over a five-decade span (1970–2020). The key findings are thus that (1) integrity-based (vs. reliability-based) antecedents are more effective in driving trust, and (2) trust is more effective in improving primarily attitudinal (vs. primarily behavioral) outcomes. Moderation analyses unpack further heterogeneity. Notably, both integrity-based and reliability-based antecedents have become stronger drivers of consumer trust in recent years. Theoretical and practical contributions are discussed in addition to advancing important future directions. [ABSTRACT FROM AUTHOR]

It is well-known that the famous Selberg integral is equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a generalization of the q-Morris constant term identity[J. Combin. Theory Ser. A 81 (1998), pp. 69–87]. This conjecture was proved and extended by Károlyi, Nagy, Petrov, and Volkov (KNPV) in 2015 [Adv. Math. 277 (2015), pp. 252–282]. In this paper, we obtain two symmetric function generalizations of the q-Baker–Forrester ex-conjecture. These include: (i) a q-Baker–Forrester type constant term identity for a product of a complete symmetric function and a Macdonald polynomial; (ii) a complete symmetric function generalization of KNPV's result. [ABSTRACT FROM AUTHOR]

Teaching music often focuses on developing musical concepts, through comparisons and discriminations. This paper contributes to the discussion on concept development in music through recognition of common elements in a situation and a shift from a local to a general level, considering theoretical approaches to mathematical generalisation. It sets to explore preschool children's understanding of tempo and its use in new musical situations. The research involved a musical intervention in six preschool classrooms. Critical incidences from focus group discussions and non-participant observation recorded children's understanding of tempo from their musical actions, drawings, responses and reflection to teacher questions. The findings highlight that children could go beyond the specific content of the activities and focus on the basic characteristics of tempo, integrating them into their song creations. A teaching approach oriented to generalisation through concept development can assist teachers to elaborate musical content and realise students' level of understanding. [ABSTRACT FROM AUTHOR]

In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned identity of Bressoud and Subbarao starting from a q-series identity of Ramanujan. In the present paper, we revisit the combinatorial arguments of Bressoud and Subbarao, and derive a more general weighted partition identity. Furthermore, with the help of a fractional differential operator, we establish a few more Bressoud–Subbarao type weighted partition identities beginning from an identity of Andrews, Garvan and Liang. We also found a one-variable generalization of an identity of Uchimura related to Bell polynomials. [ABSTRACT FROM AUTHOR]

In 2022, Defant and Kravitz introduced extended promotion (denoted ∂ ), a map that acts on the set of labelings of a poset. Extended promotion is a generalization of Schützenberger's promotion operator, a well-studied map that permutes the set of linear extensions of a poset. It is known that if L is a labeling of an n-element poset P, then ∂ n - 1 (L) is a linear extension. This allows us to regard ∂ as a sorting operator on the set of all labelings of P, where we think of the linear extensions of P as the labelings which have been sorted. The labelings requiring n - 1 applications of ∂ to be sorted are called tangled; the labelings requiring n - 2 applications are called quasi-tangled. We count the quasi-tangled labelings of a relatively large class of posets called inflated rooted trees with deflated leaves. Given an n-element poset with a unique minimal element with the property that the minimal element has exactly one parent, it follows from the aforementioned enumeration that this poset has 2 (n - 1) ! - (n - 2) ! quasi-tangled labelings. Using similar methods, we outline an algorithmic approach to enumerating the labelings requiring n - k - 1 applications to be sorted for any fixed k ∈ { 1 , ... , n - 2 } . We also make partial progress towards proving a conjecture of Defant and Kravitz on the maximum possible number of tangled labelings of an n-element poset. [ABSTRACT FROM AUTHOR]

Aposematic prey use conspicuous, high-contrast colour patterns to warn potential predators that they possess a defence mechanism, and signal uniformity is important to promote predator learning and memory retention; however, documented variation in the aposematic pattern of many species exists. Most aposematism studies use avian predators and insect prey; we know little about how mammalian predators learn about and interact with aposematic prey. For the first time, we evaluated aposematic learning in a mammalian predator–prey system. We conditioned captive coyotes, Canis latrans , to contact brown-furred models, and then trained them to avoid black-and-white models resembling striped skunks, Mephitis mephitis , that sprayed a skunk oil solution before testing their ability to generalize to variant patterns mimicking natural skunk coat variation. Coyotes exhibited great variation at all levels of the experiment but generally showed varying levels of wariness of the skunk-striped model and most effectively learned to avoid the model after being sprayed. Subsequently, whiter models elicited greater avoidance than blacker models, suggesting that the strength of the white on black signal influences coyote aposematic generalization. This pioneering study of mammalian aposematic learning suggests that more conspicuous coloration speeds learning for predator avoidance of aposematic prey and enhances generalization. • First examination of aposematic learning in a mammalian predator–prey system. • We trained coyotes to avoid skunk-striped models that sprayed skunk oil upon attack. • Coyotes displayed varying wariness of skunk-striped models. • Whiter models induced stronger avoidance than blacker models. • Pioneering study reveals coyotes' ability to learn avoidance from skunk models. [ABSTRACT FROM AUTHOR]

We introduce some generalisations of the Euler–Kronecker constant of a number field and study their arithmetic nature. [ABSTRACT FROM AUTHOR]

Savoring is a positive emotion up‐regulation technique that can increase electrocortical and self‐reported valence and arousal to positive and neutral pictures, with effects persisting to increase response to the same stimuli when encountered later. Outside of the lab, emotion regulation techniques that persist to affect not just encounters with the same stimuli but also encounters with similar, but previously unencountered stimuli should save individuals time and effort. Here, we used event‐related potentials and picture ratings to test whether savoring would generalize to similar, but previously unseen positive pictures. To this end, 89 participants (56 female; M age = 18.96 years, SD = 1.87) were asked to savor positive pictures from one category (e.g., happy people) and to view positive pictures from another category (e.g., cute animals), as well as to view neutral pictures (e.g., plants). In a subsequent passive picture viewing task, participants viewed novel pictures from all three categories (i.e., happy people, cute animals, plants). In the first task, savoring was effective for pictures of animals throughout picture presentation, but only for pictures of people during the later part of picture presentation. In the second task, savoring generalized to novel pictures of animals, though this was only evident in the early portion of picture processing (and for self‐reported ratings). Therefore, savoring holds promise as a useful technique for increasing positive emotion in everyday life, though more work is needed to understand whether effects may vary depending on different types of picture content. We tested whether savoring, a technique for increasing positive emotion, would generalize to novel, similar stimuli, thereby saving individuals time and effort. Participants performed a savor and view task, before viewing similar pictures in a passive view task. Results showed that pictures resembling those that had previously been savored elicited increased late positive potentials and more emotional ratings than pictures resembling those that had been viewed. Nonetheless, effects were specific to certain picture content. [ABSTRACT FROM AUTHOR]

In this paper, the piecewise Chebyshev cardinal functions (PCCFs) are handled to design a highly accurate direct method to solve a category of fractional optimal control problems (FOCPs) involving the Caputo–Katugampola fractional derivative (as a generalisation of the Caputo derivative) in a large domain. These cardinal functions have many useful features, such as cardinality, exponential accuracy and orthogonality. Notice that the exponential accuracy makes it possible to obtain an approximate solution with very high accuracy for the problem under consideration by applying only a small number of basis functions. In this regard, first, the ordinary and fractional integral matrices of the PCCFs are obtained to construct a direct method using them. Then, the constructed approach turns to solve the FOCP under consideration into deriving the solution of an algebraic system (by the aid of approximating the state and control variables based on the PCCFs). To show the validity of the established technique some illustrative examples are provided. [ABSTRACT FROM AUTHOR]

One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether kernel interpolation can generalize well, since it may help us understand the 'benign overfitting phenomenon' reported in the literature on deep networks. In this paper, under mild conditions, we show that, for any ε > 0 ⁠ , the generalization error of kernel interpolation is lower bounded by Ω (n − ε) ⁠. In other words, the kernel interpolation generalizes poorly for a large class of kernels. As a direct corollary, we can show that overfitted wide neural networks defined on the sphere generalize poorly. [ABSTRACT FROM AUTHOR]

We show that on super-reflexive spaces a Moreau-Yosida type of regularisation by infimal convolution together with a known insertion-type theorem (a variant of Ilmanen's lemma) easily give an approximation of a Lipschitz function by a C^{1,\alpha }-smooth Lipschitz function with the same Lipschitz constant. This is a generalisation of the well-known theorem of J.-M. Lasry and P.-L. Lions from Hilbert spaces. It also gives a new self-contained and probably simpler proof of the Lasry-Lions theorem. [ABSTRACT FROM AUTHOR]

Previous research has identified UPGRADE Your Performance as a method for teaching employment soft skills to students with disabilities. UPGRADE Your Performance instruction is a multicomponent intervention including self-evaluation, self-graphing, goal setting, and technology-aided instruction. This pilot study investigated the generalized effects of UPGRADE Your Performance on soft skills of secondary students with intellectual and other developmental disabilities participating in an 18-21 transition program located on a university campus. Results indicated that when students improved in two targeted soft skill areas, generalization occurred to three non-targeted soft skill areas. Implications for practice and suggestions for future research are included. [ABSTRACT FROM AUTHOR]

In this paper, we construct two kinds of q -differential integrable hierarchies. The first one is the q -universal character of B-type (BUC) and lattice q -BUC hierarchies expressed by q -shift operators. It is also shown that the lattice q -BUC hierarchy reduces to the q -BUC hierarchy with certain conditions. The other one is the q -deformed generalized symplectic Schur functions and the q -deformed generalized Q-functions defined by q -derivative operators. By means of the q -deformed vertex operators, the q -deformed symplectic universal character (SUC) and BUC hierarchies have been presented. Moreover, it is proved that q -deformed generalized symplectic Schur functions and generalized Q-functions are solutions of the q -deformed SUC and BUC hierarchies, respectively. Meanwhile, by using multi-component tau functions, we establish the multi-component q -deformed SUC and BUC hierarchies. In addition, based upon the discrete tau functions, the multi-component modified q -deformed SUC and BUC hierarchies have been discussed. [ABSTRACT FROM AUTHOR]

Excitable systems have important biological applications, such as impulse transmission in neurons. The Chialvo map and Rulkov map are popular and important for studying the nonlinear dynamics of neurons. Both belong to the family of two-dimensional maps used to describe excitable systems in general and neural dynamics in particular. They show rich dynamics ranging from oscillatory, bursting to chaotic bursting behaviour. Neurons have memory and extension of the above maps to fractional order is an efficient way to model the effects of memory. This generalisation provides a wider scope of understanding the neuron systems. We study the dynamics of the above maps for fractional orders. We observe that whether the chaotic range is suppressed, enhanced or remains unchanged depends on the details of the eigenvalues of Jacobian obtained by the linearisation around the fixed point. We show that the three cases studied give three different results. The impact of fractional order on the efficacy of feedback control as well as the frequency and amplitude of bursts in the chaotic region is different for different maps. Thus, the impact of memory on the stability of neuronal maps depends on the details of the underlying system. [ABSTRACT FROM AUTHOR]

First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living systems. On the other hand, modern data-driven methods thrive at modeling many types of high-dimensional and noisy data. Still, the training and interpretation of these data-driven models remain challenging. Here, we combine the two types of methods to model stochastic neuronal network oscillations. Specifically, we develop a class of artificial neural networks to provide faithful surrogates to the high-dimensional, nonlinear oscillatory dynamics produced by a spiking neuronal network model. Furthermore, when the training data set is enlarged within a range of parameter choices, the artificial neural networks become generalizable to these parameters, covering cases in distinctly different dynamical regimes. In all, our work opens a new avenue for modeling complex neuronal network dynamics with artificial neural networks. [ABSTRACT FROM AUTHOR]

Hansen (2005) obtained the efficiency bound (the lowest achievable risk) in the p-dimensional normal location model when p≥3, generalizing an earlier result of Magnus (2002) for the one-dimensional case (p = 1). The classes of estimators considered are, however, different in the two cases. We provide an alternative bound to Hansen's which is a more natural generalization of the one-dimensional case, and we compare the classes and the bounds. [ABSTRACT FROM AUTHOR]

A smoothed bootstrap method is introduced for right-censored data based on the right-censoring-A(n) assumption introduced by Coolen and Yan, which is a generalization of Hill's A(n) assumption for right-censored data. The smoothed bootstrap method is compared to Efron's method for right-censored data through simulations. The comparison is conducted in terms of the coverage of percentile confidence intervals for the quartiles. From the study, it is found that the smoothed bootstrap method mostly performs better than Efron's method, in particular for small data sets. We also illustrate the use of the method for survival function inference and compare it to a smoothed Kaplan-Meier bootstrap method through simulations. [ABSTRACT FROM AUTHOR]

In this work we propose a generalization of the family of Time-Accurate and highly-Stable Explicit (TASE) operators recently introduced by Calvo, Montijano and Rández (2021). In this family the TASE operator of order p depends on p free real parameters. Here we consider operators that can also be defined by complex parameters occurring in conjugate pairs. Despite this choice the calculations continue to be done only in real arithmetic, thus not burdening the computational cost of the previous version of the family. Conversely, this generalization leads to improve both the accuracy and stability properties of explicit Runge-Kutta schemes supplemented with TASE operators. Numerical experiments showing the competitiveness of the methods proposed in this paper with respect to classical integrators for stiff problems are also presented. [ABSTRACT FROM AUTHOR]

As a proper generalization of comultiplication modules, the concept of k-comultipli-cation semimodules is introduced in this paper. Let S be a semiring. An left S-semimodule M is called a left k-comultiplication semimodule if for each subtractive subsemimodule N of M, there exists an ideal I of S such that N = (0 : M r I) . Some properties of k-comultiplication semimodules are obtained and some conditions are given for a direct sum of k-comultiplication semimodules to be a k-comultiplication semimodule. [ABSTRACT FROM AUTHOR]

The Fundamental Theorem of Projective Geometry states that, in a vector space, a permutation of vector lines preserving triples that span a vector plane is induced by a semi-linear automorphism. We consider a generalisation to triples of subspaces, not necessarily of the same dimension, spanning, or being contained in a subspace of fixed dimension. We determine all cases in which the permutation is necessarily induced by a semi-linear automorphism. [ABSTRACT FROM AUTHOR]

Let F be a saturated fusion system on a finite p -group S , and let P be a strongly F -closed subgroup of S. We define the concept " F -essential subgroups with respect to P " which are some proper subgroups of P satisfying some technical conditions and show that an F -isomorphism between subgroups of P can be factorized by some automorphisms of P and F -essential subgroups with respect to P. When P is taken to be equal to S , the Alperin-Goldschmidt fusion theorem can be obtained as a special case. We also show that P ⊴ F if and only if there is no F -essential subgroup with respect to P. The following definition is made: A p -group P is strongly resistant in saturated fusion systems if P ⊴ F whenever there is an over p -group S and a saturated fusion system F on S such that P is strongly F -closed. It is shown that several classes of p -groups are strongly resistant, which appears as our third main theorem. We also give a new necessary and sufficient criterion for a strongly F -closed subgroup to be normal in F. These results are obtained as a consequence of developing a theory of quasi and semi-saturated fusion systems, which seems to be interesting in its own right. [ABSTRACT FROM AUTHOR]

Let X be an infinite set and I(X) the symmetric inverse semigroup on X. For a nonempty subset Y of X and an infinite cardinal q such that |X| ≥ q, let PS(X, Y, q) = {α ∈ I(X) : |X\Xα| = q and Xα ⊂ Y }. Then PS(X, Y, q) is a generalization of the partial Baer-Levi semigroup PS(X, q) = {α ∈ I(X) : |X\Xα| = q} which has been studying since 1975. In this paper, we describe the Green's relations and characterize the natural partial order on PS(X, Y, q). With respect to this partial order, we determine when two elements are related, find all the maximum, minimum, maximal, minimal, lower cover and upper cover elements. Also, we describe elements which are compatible and we investigate the greatest lower bound and the least upper bound of two elements in PS(X, Y, q). [ABSTRACT FROM AUTHOR]

This paper presents an extension of Bhargava's theory of factorials associated to any nonempty subset S of Z. Bhargava's factorials k ! S are invariants, constructed using the notion of p -orderings of S where p is a prime. This paper defines b -orderings of any nonempty subset S of Z for all integers b ≥ 2 , as well as "extreme" cases b = 1 and b = 0. It defines generalized factorials k ! S , T and generalized binomial coefficients ( k + ℓ k ) S , T as nonnegative integers, for all nonempty S and allowing only b in T ⊆ N. It computes b -ordering invariants when S is Z and when S is the set of all primes. [ABSTRACT FROM AUTHOR]

In this work we present a systematic study of n-layered modules which are closely related to Σ-modules. For each integer n ≥ 1 we prove some results for n-layered modules concerning when Σ-modules are direct sum of countably generated modules. Moreover, we discover additional restriction which leads to coinciding of n-layered modules and m-layered modules for n > m. [ABSTRACT FROM AUTHOR]

The Dowling lattice Qn(G), G a finite group, generalizes the geometric lattice generated by all vectors, over a field, with at most two nonzero components. Abstractly, it is a fundamental object in the classification of finite matroids. Constructively, it is the frame matroid of a certain gain graph known as G·K(V) n. Its Whitney numbers of the first kind enter into several important formulas. Ravagnani suggested and partially proved that these numbers of Qn(G) and higher-weight generalizations are polynomial functions of |G|. We give a simple proof for Qn(G) and its generalization to a wider class of gain graphs and biased graphs, and we determine the degrees and coefficients of the polynomials. [ABSTRACT FROM AUTHOR]

We provide generalizations of a class of stochastic Gronwall inequalities that has been studied by von Renesse and Scheutzow (2010), Scheutzow (2013), Xie and Zhang (2020) and Mehri and Scheutzow (2021). This class of stochastic Gronwall inequalities is a useful tool for SDEs. Our focus are convex generalizations of the Bihari-LaSalle type. The constants we obtain are sharp. In particular, we provide new sharp constants for the stochastic Gronwall inequalities. The proofs are connected to a domination inequality by Lenglart (1977), an inequality by Pratelli (1976) and a characterization of Lenglart's concept of domination via the Snell envelope. The inequalities we study appear for example in connection with exponential moments of solutions to path-dependent SDEs: For non-path-dependent SDEs, criteria for the finiteness of exponential moments are known. To be able to extend these proofs to the path-dependent case, a convex generalization of a stochastic Gronwall inequality seems necessary. Using the results of this paper, we obtain a criterion for the finiteness of exponential moments which is similar to that known for non-path-dependent SDEs. Stochastic Gronwall inequalities can also be applied to study other types of SDEs than path-dependent SDEs: An estimate of this paper is applied by Agresti and Veraar (2023) to prove global well-posedness for reaction-diffusion systems with transport noise. [ABSTRACT FROM AUTHOR]

In this study, Levinson-type inequalities for the class of n-convex (n ≥ 3 ) functions are generalized using new Green functions and the Hermite interpolating polynomial involving two types of data points. Some estimations for novel functionals are derived using f-divergence. Furthermore, different inequalities involving Shannon entropies are presented. [ABSTRACT FROM AUTHOR]

It is shown by tiling that only three out of the thirteen title molecules are planar. Using our recent concept of quasi-molecule ('tile') or its generalisation, all participating tiles have been here optimised in a few spin-states both at the DFT level with the B3LYP and M06-2X functionals, and using the CCSD(T) method. While borazine ( $ 1,4,6-{\rm B}_3{\rm N}_3{\rm H}_6 $ 1 , 4 , 6 − B 3 N 3 H 6 ) was synthesised in the forties of the past century, its next up-lying planar isomer ( $ 1,3,4-{\rm B}_3{\rm N}_3{\rm H}_6 $ 1 , 3 , 4 − B 3 N 3 H 6 or $ {\rm BHNHNHBHBHNH} $ BHNHNHBHBHNH ) was not. Quasi-tetratomic tiles are then shown to be shape-determining while 5-body terms and beyond are shape-preserving. The need to bring the notion of planarity as a probabilistic outcome is also examined, and the concept of planarity likelihood ratio (index) introduced. As for the above borazine isomers, this index is also predicted to be unit for $ 1,4-{\rm B}_4{\rm N}_2{\rm H}_6 $ 1 , 4 − B 4 N 2 H 6 , a result that is corroborated upon its optimisation at DFT/B3LYP/AVTZ level but not with M06-2X by which it is predicted as quasi-planar. Nevertheless, recent work with a derivative of diazatetraborinine where all atoms are bonded to substituent atoms or groups of atoms confirms the planarity of the $ {\rm B}_4{\rm N}_2 $ B 4 N 2 ring. Such a result is further corroborated at the gold-standard CCSD(T) level. Although planarity is also predicted for $ {\rm B}_6{\rm H}_6 $ B 6 H 6 , DFT and CCSD(T) frequency calculations suggest it to be likely a saddle point. [ABSTRACT FROM AUTHOR]

This study focuses on advancing the field of remote sensing image target detection, addressing challenges such as small target detection, complex background handling, and dense target distribution. We propose solutions based on enhancing the YOLOv7 algorithm. Firstly, we improve the multi-scale feature enhancement (MFE) method of YOLOv7, enhancing its adaptability and precision in detecting small targets and complex backgrounds. Secondly, we design a modified YOLOv7 global information DP-MLP module to effectively capture and integrate global information, thereby improving target detection accuracy and robustness, especially in handling large-scale variations and complex scenes. Lastly, we explore a semi-supervised learning model (SSLM) target detection algorithm incorporating unlabeled data, leveraging information from unlabeled data to enhance the model's generalization ability and performance. Experimental results demonstrate that despite the outstanding performance of YOLOv7, the mean average precision (MAP) can still be improved by 1.9%. Specifically, under testing on the TGRS-HRRSD-Dataset, the MFE and DP-MLP models achieve MAP values of 93.4% and 93.1%, respectively. Across the NWPU VHR-10 dataset, the three models achieve MAP values of 93.1%, 92.1%, and 92.2%, respectively. Significant improvements are observed across various metrics compared to the original model. This study enhances the adaptability, accuracy, and generalization of remote sensing image object detection. [ABSTRACT FROM AUTHOR]

Vertices in the graph of a square matrix over a field may be classified as to how their removal changes the geometric multiplicity of an identified eigenvalue. There are three possibilities: $ +1 $ + 1 (Parter); no change (neutral); and $ -1 $ − 1 (downer). When the graph is a tree, the 'downer branch mechanism' distinguishes the Parter vertices. Here, we discover how this mechanism generalizes for general graphs, both for Hermitian matrices and general matrices. Then, we apply the new ideas, both to classify pendent edges in general graphs, and to understand the existence of 2-downer edge cycles in general graphs, when there is a 2-downer edge. This is a further explanation of why such edges cannot occur in trees. [ABSTRACT FROM AUTHOR]

In this paper, we study unimodality conditions for distributions that describe markets with stochastic demand. Such conditions naturally emerge in the analysis of game-theoretic models of market competition (Cournot games) and supply chain coordination (Stackelberg games). We express the price elasticity of expected demand in terms of the mean residual life (MRL) function of the demand distribution and characterize optimal prices or equivalently, points of unitary elasticity, as fixed points of the MRL function. This leads to economic interpretable conditions on the demand distribution under which such fixed points exist and are unique. We find that markets with increasing price elasticity of expected demand that eventually become elastic correspond to distributions with decreasing generalized mean residual life (DGMRL) and finite second moment. DGMRL distributions strictly generalize the widely used increasing generalized failure rate (IGFR) distributions. We further elaborate on the relationship of the two classes, link their limiting behavior at infinity and examine moment and closure properties of DGMRL distributions that are important in economic applications. The DGMRL unimodality condition is useful in the analysis of optimal decisions under uncertainty in settings that are not covered by the widely-used IGFR condition; thus, it can be of broader interest to the game-theory and operations research literature. [ABSTRACT FROM AUTHOR]

In model selection problems, robustness is one important feature for selecting an adequate model from the candidates. We focus on statistical divergence-based selection criteria and investigate their robustness. We mainly consider BHHJ divergence and related classes of divergence measures. BHHJ divergence is a representative robust divergence measure that has been utilized in, for example, parametric estimation, hypothesis testing, and model selection. We measure the robustness against outliers of a selection criterion by approximating the difference of values of the criterion between the population with outliers and the non-contaminated one. We derive and compare the conditions to guarantee robustness for model selection criteria based on BHHJ and related divergence measures. From the results, we find that conditions for robust selection differ depending on the divergence families, and that some expanded classes of divergence measures require stricter conditions for robust model selection. Moreover, we prove that robustness in estimation does not always guarantee robustness in model selection. Through numerical experiments, we confirm the advantages and disadvantages of each divergence family, asymptotic behavior, and the validity for employing criteria on the basis of robust divergence. Especially, we reveal the superiority of BHHJ divergence in robust model selection for extensive cases. [ABSTRACT FROM AUTHOR]

The paper considers the classes of GSDD1, GSDD 1 ∗ , and SD-SDD matrices, which contain the class of SDD (strictly diagonally dominant) matrices and are contained in the class of nonsingular H -matrices. New upper bounds on ‖ A - 1 ‖ ∞ for GSDD1, GSDD 1 ∗ , and SD-SDD matrices A, generalizing known upper bounds for S-SDD, SDD 1 ∗ , and GSDD1 matrices, are established and compared. [ABSTRACT FROM AUTHOR]

We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three strategies (rock–paper–scissors) higher order interaction terms allow travelling waves to emerge in non-declining finite populations. We show that these travelling waves arise from diffusion stabilisation of an unstable interior equilibrium point that is present in the aspatial dynamics. Based on these observations and prior results, we offer two conjectures whose proofs would fully generalise our results to all odd cyclic games, both with and without higher order interactions, assuming a spatial replicator dynamic. Intriguingly, these generalisations for N ⩾ 5 strategies seem to require declining populations, as we show in our discussion. [ABSTRACT FROM AUTHOR]